Modelling plant disease epidemics

  • A. van Maanen
  • X.-M. Xu
Chapter

Abstract

An epidemic is the progress of disease in time and space. Each epidemic has a structure whose temporal dynamics and spatial patterns are jointly determined by the pathosystem characteristics and environmental conditions. One of the important objectives in epidemiology is to understand such spatio-temporal dynamics via mathematical and statistical modelling. In this paper, we outline common methodologies that are used to quantify and model spatio-temporal dynamics of plant diseases, with emphasis on developing temporal forecast models and on quantifying spatial patterns. Several examples of epidemiological models in cereal crops are described, including one for Fusarium head blight.

Key words

epidemiology model differential equations spatial pattern disease forecasting aggregation 

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References

  1. Ahlers D (1989) Integrated plant protection for fungus diseases in winter oilseed rape. Gesunde Pflanzen 41: 306–311Google Scholar
  2. Anderson RM and May RM (1979) Population biology of infectious diseases: part I. Nature 280: 361–367PubMedCrossRefGoogle Scholar
  3. Andrivon D and Limpert E (1992) Origin and proportions of the components of composite populations of Erysiphe graminis f.sp. hordei. Journal of Phytopathology 135: 6–19CrossRefGoogle Scholar
  4. Barajas-Aceves M, Hassan M, Tinoco R and Vazquez-Duhalt R (2002) Effect of pollutants on the ergosterol content as indicator of fungal biomass. Journal of Microbiological Methods 50: 227–236PubMedCrossRefGoogle Scholar
  5. Barrett JA (1978) A model of epidemic development in variety mixtures. In: Scott PR and Bainbridge A (eds) Plant Disease Epidemiology (pp 129–137 ) Blackwell Scientific Publications, Oxford, London, Edinburgh, MelbourneGoogle Scholar
  6. Bateman GL, Dyer PS and Manzhula L (1995) Development of apothecia of Tapesia yallundae in contrasting populations selected by fungicides. European Journal of Plant Pathology 101: 695–699CrossRefGoogle Scholar
  7. Ben-Yephed Y, Genizi A and Siti E (1993) Sclerotial survival and apothecial production by Sclerotinia sclerotiorum following outbreaks of lettuce drop. Phytopathology 83: 509–513CrossRefGoogle Scholar
  8. Beresford RM and Royle DJ (1988) Relationships between leaf emergence and latent period of leaf rust (Puccinia hordei) on spring barley, and their significance for disease monitoring. Zeitschrift fur Pflanzenkrankheiten und Pflanzenschutz 95: 361–371Google Scholar
  9. Blunt SJ, Asher MJC and Gilligan CA (1992) The effect of sowing date on infection of sugar beet by Polymyza betae. Plant Pathology 41: 148–153CrossRefGoogle Scholar
  10. Bolland GJ and Hall R (1994) Index of plant hosts of Sclerotinia sclerotiorum. Canadian Journal of Plant Pathology 16: 93–108CrossRefGoogle Scholar
  11. Brasier CM (1990) The unexpected element: Mycovirus involvement in the outcome of two recent pandemics, Dutch elm disease and chestnut blight. In: Burdon JJ and Leather SR (eds) Pests, Pathogens and Plant Communities (pp 289–307 ) Blackwell, OxfordGoogle Scholar
  12. Brasset PR and Gilligan CA (1989) Fitting of simple models for field disease progress data for the take-all fungus. Plant Pathology 38: 397–407CrossRefGoogle Scholar
  13. Burgess DR and Hepworth G (1996) Biocontrol of Sclerotinia stem rot (Sclerotinia minor) in sunflower by seed treatment with Gliocladium virens. Plant Pathology 45: 583–592CrossRefGoogle Scholar
  14. Burrough PA (1987) Spatial aspects of ecological data. In: Jongman RHG, Braak CFG and van Tongeren OFR (eds) Data Analysis in Community and Landscape Ecology (pp 213–251 ) PUDOC, Wageningen, the NetherlandsGoogle Scholar
  15. Campbell CL (1998) Disease progress in time: Modelling and data analysis. In: Gareth Jones D (ed) The Epidemiology of Plant Diseases (pp 181–206 ) Kluwer Academic Publishers, Dordrecht, the NetherlandsCrossRefGoogle Scholar
  16. Campbell CL and Madden LV (1990) Introduction to Plant Disease Epidemiology. John Wiley and Sons, New YorkGoogle Scholar
  17. Chellemi DO, Rohrbach KG, Yost RS and Sonoda RM (1988) Analysis of the spatial pattern of plant pathogen and diseased plants using geostatistics. Phytopathology 78: 221–226CrossRefGoogle Scholar
  18. Cohlbach N, Lucas P and Meynard JM (1997) Influence of crop management on take-all development and disease cycles in winter wheat. Phytopathology 87: 26–32CrossRefGoogle Scholar
  19. Correll JC, Gordon TR and Elliott VJ (1988) Powdery mildew on tomato: The effect of planting date and triadimefon on disease onset, progress, incidence, and severity. Phytopathology 78: 512–519Google Scholar
  20. de Vallavieille-Pope C, Giosue S, Munk L, Newton AC, Niks RE, Ostergard H, Pons-Kuhnemann J, Rossi V and Sache I (2000) Assessment of epidemiological parameters and their use in epidemiological and forecasting models of cereal airborne diseases. Agronomie 20: 715–727CrossRefGoogle Scholar
  21. de Vallavieille-Pope C, Huber L, Leconte M and Goyeau H (1995) Comparative effects of temperature and interrupted wet periods on germination, penetration andinfection of Puccinia recondita f.sp. tritici and P. striiformis urediniospores on wheat seedlings. Phytopathology 85: 409–415CrossRefGoogle Scholar
  22. De Wolf ED, Madden LV and Lipps PE (2000) Risk assessment models for wheat Fusarium head blight. Phytopathology 90: S19Google Scholar
  23. Dix NJ and Webster J (1995) Fungal Ecology. Chapman and Hall, London, New York, USAGoogle Scholar
  24. Ferrandino FJ (1993) Dispersive epidemic waves. I. Focus expansion in a linear planting. Phytopathology 83: 795–802CrossRefGoogle Scholar
  25. Ferrandino FJ (1996) Length scale of disease spread: Fact or artefact of experimental geometry. Phytopathology 86: 806–811Google Scholar
  26. Ferrandino FJ (1998) Past non-randomness and aggregation to spatial correlation: 2DCORR, a new approach for discrete data. Phytopathology 88: 84–91PubMedCrossRefGoogle Scholar
  27. Fitt BDL, Gregory PH, Todd AD, McCartney HA and MacDonald OC (1987) Spore dispersal and plant disease gradients: A comparison between two empirical models. Journal of Phytopathology 118: 227–242Google Scholar
  28. Fleiss JL (1981) Statistical Methods for Rates and Proportions, 2nd edn. Wiley, New York, USAGoogle Scholar
  29. Fleming RA (1980) The potential for control of cereal rust by natural enemies. Theoretical Population Biology 18: 374–395CrossRefGoogle Scholar
  30. Francl LJ and Panigrahi S (1997) Artificial neural network models of wheat leaf wetness. Agricultural and Forest Meteorology 88: 57–65CrossRefGoogle Scholar
  31. Francl LJ, Panigrahi S, Pahdi T, Gillespie TJ and Barr A (1995) Neural network models that predict leaf wetness. Phytopathology 85: 1128Google Scholar
  32. Gibson GJ (1997) Markov Chain Monte Carlo methods for fitting spatiotemporal stochastic models in plant epidemiology. Applied Statistics 46: 215–233Google Scholar
  33. Gilligan CA (1985) Mathematical modelling of crop disease. In: Gilligan CA (ed) Advances in Plant Pathology, Vol 3 (p 255 ) Academic Press, Inc, New YorkGoogle Scholar
  34. Gottwald TR (1995) Spatio-temporal analysis and isopath dynamics of citrus scab in nursery plots. Phytopathology 85: 1082–1092CrossRefGoogle Scholar
  35. Gottwald TR, Avinent L, Llacer G, Hermoso de Mendoza A and Cambra M (1995) Analysis of spatial spread of sharka (plum pox virus) in apricot and peach orchards in eastern Spain. Plant Disease 79: 266–278CrossRefGoogle Scholar
  36. Gottwald TR, Cambra M, Moreno P, Camarasa E and Piquer J (1996) Spatial and temporal analysis of citrus tristeza virus in eastern Spain. Phytopathology 86: 45–55CrossRefGoogle Scholar
  37. Gourbiere F, Gourbiere S, van Maanen A, Vallet G and Auger P (1999) Proportion of needles colonised by one fungal species in coniferous litter: The dispersal hypothesis. Mycological Research 103: 353–359Google Scholar
  38. Gray SM, Moyer JW and Bloomfield P (1986) Two-dimensional distance class model for quantitative description of virus-infected plant distribution lattices. Phytopathology 76: 243–248CrossRefGoogle Scholar
  39. Gumpert F-M, Geiger HH and Stahle U (1987) A mathematical model of the epidemics in homogeneous and heterogeneous host stands. Zeitschrift fuer Pflanzenkrankheiten und Pflanzenschutz 94: 206–215Google Scholar
  40. Gutierrez AP, DeVay JE and Frieverthauser GE (1983) A model of Verticillium wilt in relation to cotton growth and development. Phytopathology 73: 89–95CrossRefGoogle Scholar
  41. Hardwick NV (1998) Disease forecasting. In: Gareth Jones D (ed) The Epidemiology of Plant Diseases (pp 207–230 ) Kluwer Academic Publishers, Dordrecht, the NetherlandsCrossRefGoogle Scholar
  42. Hosford RM Jr, Larez CR and Hammond JJ (1987) Interactions of wet periods and temperature on Pyrenophora tritici-repentis infection and development in wheats of different resistance. Phytopathology 77: 1021–1027CrossRefGoogle Scholar
  43. Huber L and Gillespie TJ (1992) Modelling leaf wetness in relation to plant disease epidemiology. Annual Review of Phytopathology 30: 553–577CrossRefGoogle Scholar
  44. Hughes G and Madden LV (1992) Aggregation and incidence of disease. Plant Pathology 41: 657–660CrossRefGoogle Scholar
  45. Hughes G and Madden LV (1993) Using the beta-binomial distribution to describe aggregated patterns of plant disease incidence. Phytopathology 83: 759–763CrossRefGoogle Scholar
  46. Hughes G, Madden LV and Munkvold GP (1996) Cluster sampling for disease incidence data. Phytopathology 86: 132–137Google Scholar
  47. Hughes G, McRoberts N, Madden LV and Nelson SC (1997) Validating mathematical models of plant-disease progress in space and time. IMA Journal of Mathematics Applied in Medicine and Biology 14: 85–112CrossRefGoogle Scholar
  48. Ingold CT (1971) Fungus Spores: Their Liberation and Dispersal. Clarendon Press, OxfordGoogle Scholar
  49. Ingold CT (1978) Role of mucilage in dispersal of certain fungi. Transactions of the British Mycological Society 70: 137–140CrossRefGoogle Scholar
  50. Jamaux I and Spire D (1994) Development of a polyclonal antibody-based immunoassay for the early detection of Sclerotinia sclerotiorum in rapeseed petals. Plant Pathology 43: 847–862CrossRefGoogle Scholar
  51. Jeger MJ (1986) The potential of analytic compared with simulation approaches to modelling in plant disease epidemiology. In: Leonard K and Fry W (eds) Plant Disease Epidemiology, Population Dynamics and Management, Vol 1 (pp 255–281 ) Macmillan, New York, USAGoogle Scholar
  52. Jeger MJ (2000) Theory and plant epidemiology. Plant Pathology 49: 651–658CrossRefGoogle Scholar
  53. Jeger MJ and Tamsett J (1983) The status of models in crop protection: An analysis using data base systems. WPRS Bulletin IV - 2: 57–76Google Scholar
  54. Jeger MJ and Viljanen-Rollinson SLH (2001) The use of the area under the disease-progress curve (AUDPC) to assess quantitative disease resistance in crop cultivars. Theoretical and Applied Genetics 102: 32–40CrossRefGoogle Scholar
  55. Jeger MJ, Griffiths E and Jones DG (1981a) Effect of cereal cultivar mixtures on disease epidemics caused by splash-dispersed pathogens. In: Jenkyn JF and Plumb RT (eds) Strategies for the Control of Cereal Disease (pp 81–88 ) Blackwell Scientific Publications, Oxford, UKGoogle Scholar
  56. Jeger MJ, Jones DG and Griffiths E (1981b) Disease progress of non-specialised fungal pathogens in intraspecific mixed stands of cereal cultivars. II. Field experiments. Annals of Applied Biology 98: 199–210Google Scholar
  57. Jeger MJ, VanDenBosch F, Madden LV and Holt J (1998) A model for analysing plant-virus transmission characteristics and epidemic development. IMA Journal of Mathematics Applied in Medicine and Biology 15: 1–18CrossRefGoogle Scholar
  58. Johnson DA (1980) Effect of low temperature on the latent period of slow and fast rusting winter wheat genotypes. Plant Disease 64: 1006–1008CrossRefGoogle Scholar
  59. Johnson BN and McGill WB (1990) Comparison of ergosterol and chitin as quantitative estimates of mycorrhizal infection and Pinus contorta seedlings response to inoculation. Canadian Journal of Forest Research 20: 1125–1131CrossRefGoogle Scholar
  60. Kampmeijer P and Zadocks JC (1974) A simulator of foci and epidemics in mixtures, multilines and mosaics of resistant and susceptible plants. Simulation Monograph (p 50 ) Pudoc, Wageningen, the NetherlandsGoogle Scholar
  61. Kotliar N and Wiens J (1990) Multiple scales of patchiness and patch structure: A hierarchical framework for the study of heterogeneity. Oikos 59 (2): 253–260CrossRefGoogle Scholar
  62. Kranz J (1975) Beziehungen zwischen Blattmasse und Befallsentwicklung bei Blatt Krankheiten. Zeitschrift fur Planzenkrankeiten und Pflanzenschutz 82: 641–654Google Scholar
  63. Kranz J and Royle DJ (1978) Perspectives in mathematical modelling of plant disease epidemics. In: Scott PR and Bainbridge A (eds) Plant Disease Epidemiology (pp 111–120 ) Blackwell Scientific Publications, Oxford, London, Edinburgh, MelbourneGoogle Scholar
  64. Lacey J (1996) Spore dispersal–its role in ecology and disease: The British contribution to fungal aerobiology. Mycological Research 100: 641–660CrossRefGoogle Scholar
  65. Lalancette N and Hickey KD (1986) Disease progression as a function of plant growth. Phytopathology 76: 1171–1175CrossRefGoogle Scholar
  66. Lefol C and Morrall RAA (1996) Immunofluorescent staining of Sclerotinia ascospores on canola petals. Canadian Journal of Plant Pathology 18: 237–241CrossRefGoogle Scholar
  67. MacHardy WE (1996) Apple Scab: Biology, Epidemiology, and Management. American Phytopathological Society, St. Paul, MN, USAGoogle Scholar
  68. Madden LV (1992) Rainfall and dispersal of fungal spores. Advances in Plant Pathology 8: 29–79Google Scholar
  69. Madden LV and Hughes G (1995) Plant disease incidence: Distributions, heterogeneity, and temporal analysis. Annual Review of Phytopathology 33: 529–564PubMedCrossRefGoogle Scholar
  70. Madden LV, Nault LR, Murral DJ and Apelt MR (1995) Spatial pattern analysis of the incidence of aster yellows disease in lettuce. Researches on Population Ecology 37: 279–289CrossRefGoogle Scholar
  71. Maddison AC, Holt J and Jeger MJ (1996) Spatial dynamics of a monocyclic disease in a perennial crop. Ecological Modelling 88: 45–52CrossRefGoogle Scholar
  72. McCartney HA (1997) The influence of environment on the development and control of disease. In: Rechcigl J (ed) Environmentally Safe Approaches to Crop Disease Control (pp 3–31 ) CRC Press, Bocan Ratan, Florida, USAGoogle Scholar
  73. McCartney HA and Fitt BDL (1998) Disease spread: Modelling development of loci. In: Gareth Jones D (ed) The Epidemiology of Plant Diseases (pp 137–160 ) Kluwer Academic Publishers, Dordrecht, the NetherlandsGoogle Scholar
  74. McMullen M, Jones R and Gallenburg D (1997) Scab of wheat and barley: A re-emerging disease of devastating impact. Plant Disease 81: 1340–1348Google Scholar
  75. Mence MJ and Hildebrandt AC (1966) Resistance to powdery mildew in rose. Annals of Applied Biology 58: 309–320CrossRefGoogle Scholar
  76. Minogue KP and Fry WE (1983a) Models for the spread of disease: Model description. Phytopathology 73: 1168–1172CrossRefGoogle Scholar
  77. Minogue KP and Fry WE (1983b) Models for the spread of disease: Some experimental results. Phytopathology 73: 1173–1176CrossRefGoogle Scholar
  78. Nelson SC (1995) Spatiotemporal distance class analysis of plant disease epidemics. Phytopathology 85: 37–43CrossRefGoogle Scholar
  79. Nelson SC, Marsh PL and Campbell CL (1992) 2DCLASS, atwodimensional distance class analysis software for the personal computer. Plant Disease 76: 427–432Google Scholar
  80. Newton AC (1989) Measuring the sterol content of barley leaves infected with powdery mildew as a means of assessing partial resistance to Erysiphe graminis f.sp. hordei. Plant Pathology 38: 534–540CrossRefGoogle Scholar
  81. Newton AC and McGurk L (199 1) Recurrent selection for adaptation of Erysiphe graminis f.sp. hordei to partial resistance and the effect on expression of partial resistance of barley. Journal of Phytopathology 132: 328–338Google Scholar
  82. Nicholson P, Turner AS, Edwards SG, Bateman GL, Morgan LW, Parry DW, Marshall J and Nuttall M (2002) Development of stem-base pathogens on different cultivars of winter wheat determined by quantitative PCR. European Journal of Plant Pathology 108: 163–177CrossRefGoogle Scholar
  83. Norton GA, Holt J and Mumford JD (1993) Introduction to pest models. In: Norton GA and Mumford JD (eds) Decision Tools for Pest Management (pp 89–99 ) CAB International, Cambridge, UKGoogle Scholar
  84. Obst A, Lepschy-von Gleissenthall J and Beck R (1997) On the aetiology of Fusarium head blight of wheat in South Germany–preceding crops, weather conditions for inoculum production and head infection, proneness of the crop to infection and mycotoxin production. Cereal Research Communications 25: 699–703Google Scholar
  85. Perry JN (1995) Spatial-analysis by distance indexes. Journal of Animal Ecology 64: 303–314CrossRefGoogle Scholar
  86. Perry JN (1998) Measures of spatial pattern for counts. Ecology 79: 1008–1017CrossRefGoogle Scholar
  87. Pielou EC (1977) Mathematical Ecology. Wiley, New YorkGoogle Scholar
  88. Rabbinge R and Bastiaans L (1989) Combination models, crop growth and pests and diseases. In: Rabbinge R, Ward SA and van Laar HH (eds) Simulation and System Management in Crop Protection (pp 217–240 )Google Scholar
  89. Pudoc, Wageningen, the Netherlands Ridout MS and Xu X-M (2000) Relationships between several quadrat-based statistical measures used to characterise spatial aspects of data on disease incidence. Phytopathology 90: 568–575Google Scholar
  90. Ridout MS, Dem~etrio CGB and Firth D (1999) Estimating intraclass correlation for binary data. Biometrics 55: 137–148Google Scholar
  91. Rogers MN (1959) Some effects of moisture and host plant susceptibility on the development of powdery mildew of roses caused by Sphaerotheca pannosa var. rosae. Memoir of the Cornell University Agricultural Experiment Station, 363, 38 ppGoogle Scholar
  92. Rossi V, Racca P, Giosue S, Pancaldi D and Alberti I (1997) A simulation model for the development of brown rust epidemics in winter wheat. European Journal of Plant Pathology 103: 453–465CrossRefGoogle Scholar
  93. Savary S, Willocquet Land Teng P (1997) Modelling sheath blight epidemics in rice tillers. Agricultural Systems 55: 359–384CrossRefGoogle Scholar
  94. Segarra J, Jeger M and van den Bosch F (2001) Epidemic patterns and dynamics of plant disease. Phytopathology 91: 1001–1010PubMedCrossRefGoogle Scholar
  95. Shaw MW (1998) Pathogen population dynamics. In: Jones DG (ed) The Epidemiology of Plant Diseases (pp 161–180 ) Kluwer Academic Publishers, Dordrecht, the NetherlandsCrossRefGoogle Scholar
  96. Shtienberg D (2000) Modelling: The basis for rationale disease management. Crop Protection 19: 747–752CrossRefGoogle Scholar
  97. SiefertRP (1981) Applications of a mycological database to principles and concepts of population and community ecology. In: Wicklow DT and Carroll GC (eds) The Fungal Community, its Organisation and Role in the Ecosystem Mycological Series, Vol 2 (pp 11–23 ) Marcel Dekker, Inc., New York, USAGoogle Scholar
  98. Stein A, Kocks CG, Zadoks JC, Frinking HD, Ruissen MA and Myers DE (1994) A geostatistical analysis of the spatiotemporal development of downy mildew epidemics in cabbage. Phytopathology 84: 1227–1239CrossRefGoogle Scholar
  99. Sutherst RW (1993) Role of modelling in sustainable pest management. In: Corey S, Dall D and Milne W (eds) Pest Control and Sustainable Agriculture (pp 66–71 ) CSIRO, AustraliaGoogle Scholar
  100. Taylor LR (1961) Aggregation, variance and the mean. Nature 189: 732–735CrossRefGoogle Scholar
  101. Thomas P (1984) Sclerotinia stem rot checklist. In: Canola Council of Canada (ed) Canola Growers Manual (pp 1053–1055 ) Minipeg, USAGoogle Scholar
  102. Tomerlin JR, Eversmeyer MG, Kramer CL and Browder LE (1983) Temperature and host effects on latent and infectious periods and on urediniospore production of Puccinia recondita f.sp. tritici. Phytopathology 73: 414–419CrossRefGoogle Scholar
  103. Turkinson TK and Morrall RAA (1993) Use of petal infestation to forecast Sclerotinia stem rot of canola: The influence of inoculum variation over the flowering period and canopy density. Phytopathology 83: 682–689CrossRefGoogle Scholar
  104. Twengstrom E, Sigvald R, Svensson C and Yuen J (1998) Forecasting Sclerotinia stem rot in spring sown oilseed rape. Crop Protection 17: 405–411CrossRefGoogle Scholar
  105. Van den Bosch F, Zadoks JC and Metz JAJ (1988) Focus expansion in plant disease. I: The constant rate focus expansion. Phytopathology 78: 55–58Google Scholar
  106. Van der Plank JE (1960) Analysis of epidemics. In: Horsfall JG and Cowling EB (eds) Plant Pathology: An Advance Treatise, Vol 3 (pp 229–289 ) Academic Press, New York, USAGoogle Scholar
  107. Van der Plank JE (1963) Plant Diseases: Epidemics and Control (p 344 ) Academic Press, New York, LondonGoogle Scholar
  108. Van der Plank JE (1982) Host-Pathogen Interactions in Plant Disease. Academic Press, New York, USAGoogle Scholar
  109. van Maanen A and Gourbiere F (2000) Balance between colonisation and fructification in fungal dynamics control: A case study of Lophodermium pinastri on Pinus sylvestris needles. Mycological Research 104: 587–594CrossRefGoogle Scholar
  110. van Maanen A, Debouzie D and Gourbiere F (2000) Distribution of three fungi colonising fallen Pinus sylvestris needles along altitudinal transects. Mycological Research 104: 1133–1138CrossRefGoogle Scholar
  111. Vloutoglou I, Fitt BDL and Lucas JA (1995) Periodicity and gradients in dispersal of Alternaria linicola in linseed crops. European Journal of Plant Pathology 101: 639–653CrossRefGoogle Scholar
  112. Waggoner PE (1986) Progress curves of foliar diseases: Their interpretation and use. In: Leonard KJ and Fry WE (eds) (pp 3–37) MacMillan, New York, USAGoogle Scholar
  113. Waggoner PE and Horsfall JG (1969) E.P.I.D.E.M.: A simulator of plant disease written for a computer. Connecticut Agricultural Experimental Station Bulletin, USA, 698Google Scholar
  114. Walters KFA and Hardwick NV (2000) Principles of pest and disease management in crop protection. In: Alford DV (ed) Pest and Disease Management Handbook (pp 1–18 ) Blackwell Science, OxfordCrossRefGoogle Scholar
  115. Webb CR, Gilligan CA and Asher MJC (2000) Modelling the effect of temperature on the development of Polymyxa betae. Plant Pathology 49: 600–607CrossRefGoogle Scholar
  116. Xu X-M (1999) Effects of temperature on the length of the incubation period of rose powdery mildew (Sphaerotheca pannosa var. rosae). European Journal of Plant Pathology 105: 13–21CrossRefGoogle Scholar
  117. Xu X-M and Ridout MS (1998) Effects of initial epidemic conditions, sporulation rate, and spore dispersal gradient on the spatio-temporal dynamics of plant disease epidemics. Phytopathology 88: 1000–1012PubMedCrossRefGoogle Scholar
  118. Xu X-M and Ridout MS (2000a) Effects of quadrat size and shape, initial epidemic conditions, and spore dispersal gradient on the spatio-temporal statistics of plant disease. Phytopathology 90: 738–750PubMedCrossRefGoogle Scholar
  119. Xu X-M and Ridout MS (2000b) Stochastic simulation of the spread of race specific and non-specific aerial fungal pathogens in cultivar mixtures. Plant Pathology 49: 207–218Google Scholar
  120. Xu X-M and Ridout MS (2001) Effects of prevailing wind direction on spatial statistics of plant disease epidemics. Journal of Phytopathology 149: 155–166CrossRefGoogle Scholar
  121. Xu X-M and Robinson JD (2000) The effects of temperature on the incubation and latent periods of hawthorn powdery mildew (Podosphaera clandestina). Plant Pathology 49: 791–797CrossRefGoogle Scholar
  122. Xu X-M and Robinson JD (2001) The effects of temperature on the incubation and the latent periods of the clematis powdery mildew (Erysiphe polygoni). Journal of Phytopathology 149: 565–568CrossRefGoogle Scholar
  123. Xu X-M, Robinson JD, Berrie AM and Harris DC (2001) Spatio-temporal dynamics of brown rot (Monilinia fructigena) on apple and pear. Plant Pathology 50: 569–578CrossRefGoogle Scholar
  124. Yang XB (1995) Analysis of variance–mean relationships of plant diseases. Journal of Phytopathology 143: 513–518CrossRefGoogle Scholar
  125. Zawolek MW and Zadoks JC (1992) Studies in focus development: An optimum for dual dispersal of plant pathogens. Phytopathology 82: 1288–1297CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • A. van Maanen
    • 1
  • X.-M. Xu
    • 2
  1. 1.Department of Environmental Resource Management, Faculty of AgricultureUniversity College DublinBelfield, Dublin 4Ireland
  2. 2.Entomology and Plant Pathology DepartmentHorticulture Research InternationalEast Malling, West Malling, KentUK

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